Download 10.2- Arithmetic vs. Geometric Sequences

Integrated Math 1 Extended - Unit 10
Name: __________________________
Date: _____________ Period: ______
10.2- Arithmetic vs. Geometric Sequences
Objective: To use a list of values or equation to determine whether a sequence is arithmetic or
geometric.
Warm-up:
Consider the sequence. Is the sequence arithmetic, geometric or neither? Justify your reasoning.
A.)
5, 10, 20, 40,…
B.)
4, 15, 26, 37, 48, …
VOCABULARY:
Sequence: the set of all numbers that follow a specific pattern

𝑎𝑛 is the correct notation to describe a rule
Term:

𝑎1 means the first term in the sequence, 𝑎2 means the second term in the sequence, etc…
Arithmetic (Linear) Sequence:


a sequence of numbers that has a constant number added or subtracted
there is only one “n” in your equation and it is not an exponent (not including the n from
𝑎𝑛 )
Geometric (Exponential) Sequence:


a sequence of numbers that is always multiplied by a constant number
there is only one “n” in your equation and it is an exponent (not including the n from 𝑎𝑛 )
**TO BE ARITHMETIC OR GEOMETRIC “n” CAN NOT BE IN THE DENOMINATOR**
Example #1:
Describe the pattern of the following numbers or pictures
A.) 15, 18, 21, 24, 27,…
B.) 2, 8, 32, 128,…
1
C.) 8, 4, 2, 1, 2,…
D.)
At the beginning
At one minute
At two minutes
At three minutes
At four minutes
E.)
Step 1
Step 2
Step 3
What are the differences between linear and exponential functions?
LINEAR
Equation (Function)
Rate of Change
Initial Value
What mathematical
operation does the
rate represent?
Create a table of
values
What does the graph
look like?
Write a situation that
represents that
function.
EXPONENTIAL
Example #2:
Example #2:
Determine if the sequence of numbers demonstrates Arithmetic, Geometric or neither. Justify
your answer.
A.) 40, 47, 54, 61, 68,…
B.) -4, 12, -36, 108, -324,…
C.) 30, 15, 7.5, 3.75,…
D.) 4,
E.) 1, 2, 4, 7, 11, 16, …
F.) 82, 76, 70, 64, 58,…
13 14
16
3
3
,
3
,5,
,…
Example #3:
Determine if function (equation) demonstrates Arithmetic, Geometric or neither. Justify your
answer.
A.) 𝑎𝑛 = 16 + 3𝑛
B.) 𝑎𝑛 = −4 ∙ (−3)𝑛−1
C.) 𝑎𝑛 = −163 + 200𝑛
D.) 𝑎𝑛 = (2𝑛)2
1 𝑛
E.) 𝑎𝑛 = −4 (19) +7
F.) 𝑎𝑛 =
14.5678
𝑛
Example #4:
Draw the next term if this represents
an arithmetic sequence.
Draw the next term if this represents
a geometric sequence.
Find the number of cubes in the next
three figures.
Find the number of cubes in the next
three figures.
Example #5:
For each sequence, state if it is arithmetic, geometric, or neither. If it is arithmetic or geometric
find the next two terms in the sequence.
A.) -3, -18, -108, -648, -3888, …
B.) 2, 4, 12, 48, 240, …
C.) -35, 165, 365, 565, 765, …
D.) -2, 6, -18, 54, -162, …
E.) -7, 143, 293, 443, 593, …
F.) 8, 14, 20, 26, 31
G.) -1, -2, -6, -24, -120, …
H.) -18, -12, -6, 0, 6, …